Problem 47 - Elementary and Intermediate Algebra

Question

Translate to an algebraic expression. Panya's speed minus twice the wind speed

Step-by-Step Solution

Answer

The algebraic expression is \(p - 2w\).

Step 1: Understand the Problem

Identify the elements involved. We have Panya's speed and the wind speed.

Step 2: Assign Variables

Let Panya's speed be represented by the variable \(p\). Let the wind speed be represented by the variable \(w\).

Step 3: Formulate the Expression

We need to form an expression for 'Panya's speed minus twice the wind speed'. This translates to \(p - 2w\).

Key Concepts

variables

In algebra, a **variable** is a symbol that represents an unknown or changeable value. Variables are essential since they allow us to work with and solve equations involving unknown quantities.
For example: In the exercise, we've used variables to represent speeds.
Panya's speed is represented by the variable \( p \). The wind speed is represented by the variable \( w \).

• **Use of Variables: ** Variables like \( p \) and \( w \) make mathematical expressions more general and flexible.
• **Operations Involving Variables:** We can add, subtract, multiply, and divide variables just like numbers.

So, variables serve as placeholders that make it possible to perform algebraic operations.

translation

Translation in algebra involves converting words or real-world scenarios into mathematical expressions. This process helps to simplify and solve problems.
In the given exercise, we translated 'Panya's speed minus twice the wind speed' into an algebraic expression by identifying key elements and using variables.
Here's how:

• **Identify Key Terms:** 'Panya's speed' corresponds to \( p \), and 'wind speed' corresponds to \( w \).
• **Understand Operations:** 'Minus' indicates subtraction, and 'twice' means to multiply by 2.

Therefore, 'Panya's speed minus twice the wind speed' translates to \( p - 2w \).
This step-by-step process ensures that words are accurately converted into mathematical language, making it easier to work with complex problems.

algebra

Algebra is a branch of mathematics that uses symbols, usually letters, to represent numbers. This field of math allows us to generalize arithmetic operations and solve equations efficiently.
In the exercise, we used algebra to create an expression for a real-world situation: Panya's speed affected by wind speed.

• **Algebraic Expressions:** These are combinations of variables, numbers, and operations. In our case, \( p - 2w \) is an algebraic expression.
• **Simplification:** Complex real-world problems can be simplified using algebra. By using the expression \( p - 2w \), we can easily calculate values if we know the speeds.

Algebra is powerful because it helps us understand and solve problems involving unknown quantities systematically.